cos(π/3-α)=cosπ/3cosα+sinπ/3sinα=1/2cosα+(根号3)/2*sinα=1/8
cosα+（根号3）sinα=2*1/8=1/4
因为cosα-cosβ=1/2,sinα-sinβ=1/3,所以
(cosα-cosβ)^2=1/4,(sinα-sinβ)^2=1/9
(cosα)^2-2cosαcosβ+(cosβ)^2=1/4,(sinα)^2-2sinαsinβ+(sinβ)^2=1/9
两式相加
(cosα)^2-2cosαcosβ+(cosβ)^2+(sinα)^2-2sinαsinβ+(sinβ)^2=1/4+1/9
因为(cosα)^2+(sinα)^2=1,(cosβ)^2+(sinβ)^2=1
所以1+1-2cosαcosβ-2sinαsinβ=1/9+1/4
2(cosαcosβ+sinαsinβ)=2-1/4-1/9
2(cosαcosβ+sinαsinβ)=59/36
2cos(α-β)=59/36
cos(α-β)=59/72
第二题题目不是题目写错就是问题有问题
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